1st of all, I am no expert in using Progression Chart or Muntha for prediction and what I am going to share is my very little knowledge on these topics. Also, there is every possibility that I may commit some mistake in explaining it because of the same reason that I am not a regular in using these tricks. So, please don't treat this post as final word on this concept.

Progression Chart - This is one of the many ways of making predictions in Astrology. Just like dashas and transits are most commonly used ways of making predictions, Progression Chart can also be one of the important ways of making predictions. As always, all the systems, methods or ways compliment each other rather than compete with each other.

Concept - So, progression chart by name itself shows some progress or evolution astrologically. The concept says that your birth chart has planets at certain degrees in certain signs at the time of native's birth. Now, the next year after birth, all the planets will be treated/considered as moved ahead (progressed or evolved) by 1 degree and same thing continues for years to come as long as individual is here in this world in human life. Important thing here is that only planets will progress and not ascendant. Ascendant of birth chart will remain as is.

Example - It is always better to understand any concept with example and when it comes to giving example, I prefer putting my chart on display - https://www.astrosaxena.com/Astrologer . As we can see, I was born with Scorpio ascendant, Venus at 6.57 deg Sagittarius, Sun at 22.53 deg/Mercury at 20.22 degree/Mars at 19.06 deg Capricorn, Ketu at 25.5 deg Aquarius, Moon at 13.58 deg Taurus, Jupiter at 8.53 deg Cancer and Saturn at 18.48 deg/Rahu at 25.46 deg Leo.

Now, if we apply the concept of progression then after 1 year of my birth, all these planets move ahead by 1 degree in their respective signs in Progression Chart of next year after birth. Then as the years progress by one after the other, all planets will continue to add 1 degree more to the last year's Progression Chart degrees. I hope it is understandable.

The Message - I think the message or purpose behind Progression Chart is evolution or improvement with time. Suppose I committed a mistake at 15 years of age and if I repeat the same mistake at 25 years of age, then what did I do in these 10 years? So, the purpose of progression chart is that we should grow, learn, evolve and reach the next level as the planets also move to the next degree.

How to read it? - Now, the main thing is how to read a Progression Chart? Normally, it is considered to read someone's annual predictions but I feel it should be more significant than just that. Let's understand it with example of my Sun's position and how my Career & Self progressed with changing position of Sun in Progression chart -

• I was born with Sun at 22.53. As per my earliest memory, I found myself at my maternal grandparents home around 6-7 years of age. Around that age, Sun in progression chart reached up to the end of 3rd house/Capricorn and was about to enter in 4th house/Aquarius of Mother or Mother side relatives. I remained disconnected from Father as Sun loses its Dig Bala in 4th house plus I have Ketu at 25 degree in my 4th house. So, we can say that Progression Sun was conjunct Ketu. It was also time when I had no idea about myself or what I was going to do in life? These things we can easily associate with Sun in 4th house/Aquarius (enemy sign) with Ketu.
• Now, 1st big change came when I entered 25th year of life. At that age, Sun in Progression Chart must be at 18 degree Aquarius and I have Saturn at 18 degree Aquarius in birth chart in 10th house/Leo of Career. Sun-Saturn both represent Law and Govt. I started legal practice but not with much success.
• Then when I was at 31st year of life when Sun in Progression Chart must be at about 25 degrees, I lost my father and career of Law. Reason? I have Ketu at 25 degrees in 4th house/Aquarius in birth chart. Ketu is separation and there was separation from everything that Sun represents.
• After an year, as Sun crossed Ketu's 25 degree and reached 26th degree in Progression Chart, I got my 1st corporate job. May be, for the 1st time I got some clear direction in Career matters. Reason? Progressed Sun had crossed Ketu's degree of birth chart. Hence, time for illusion was over.
• Then as Sun was still in degrees of Purva Bhadra Nakshatra (of mystical subjects) in Progression Chart, I started learning Astrology, unknowingly that I was going to take it as profession after couple of years.
• Then Sun at 30th degree of Aquarius and about to go into 5th house/Pisces, I quit my job and came into career of spiritual matters and counselling. 5th house is also 8th from 10th house, which represents change in career. 
• So, we can see that it is not only about your annual prediction of one year but progression chart can actually help us in understanding how life can unfold in years to come, especially if it is entering into a house/sign, nakshatra and touching the degrees of your natal planets. May be, if we take into consideration the annual transit planets and their degrees then it may be more accurate. Not to forget that we only considered Sun here. There are other 8 planets in chart and they will also indicate towards some results or events in our lives as they move ahead in progression chart.

Finally, I again say that I can get the same events and conclusions from normal vimshottari dasha and transits in my chart. So, it is not that Progression Chart is overpowering Dasha/Transits or Dasha/Transits are better than Progression. They all compliment each other rather than conflict with each other. We should understand the basic aim of Progression Chart, i.e. Evolution.

Muntha - Just like Progression Chart, there is another way which gives importance for annual progression of chart and seeing the results accordingly. This is known as Muntha. We can say that Progression Chart is more popular in Western Astrology and Muntha is more utilized in Vedic Astrology.

Concept - Good thing is that Muntha is not much complicated to understand. It is an imaginary point which remains at your ascendant and ascendant degree at the time of your birth. Then with every passing year, Muntha will shift to the next house/sign. Like, if someone is born with Cancer ascendant then for 1st year of his life Muntha will be in 1st house/Cancer. For 2nd year, Muntha will shift to 2nd house/Leo. Like this, Muntha will continue to shift into next house/sign and will complete 12 signs in 12 houses in 12 years and returns to ascendant on 13th year.

Again, I am no expert in these concepts. So, please feel free to correct if I made any mistake or add if you have more/better information on these topics.