Some common probability distributions; From here
Uniform distribution (discrete) - You rolled 1 die and the probability of falling any of 1, 2, 3, 4, 5 and 6 is equal.
Uniform distribution (continuous) - You sprayed some very fine powder towards an wall. For a small area on wall, the chances of falling dust on a spot on the wall is uniform.
You have a big cylinder of gas. For any unit area, number of gas molecules hitting per square cm on the inner wall per second, is seemingly to be uniform.
Bernoulli distribution - Bernoulli trial is (or binomial trial) is a random experiment with exactly two possible outcomes, "success" and "failure". In such a trial, probability of success is p, probability of failure is q=1-p.
For example, in a coin toss, we can have 2 outcome- head or tail. For a fair coin, probability of head is 1/2; probability of tail is 1/2 it is one kind of Bernoulli distribution which is also uniform.
In a coin toss if the coin is unfair such as probability of getting head is 0.9 then the probability of falling a tail will be 0.1.
Bernauli Distribution with probabilities 0.6 and 0.4; from here
Binomial distribution - If a Bernoulli trial (with 2 outcome, respectively with probabilities p and q=1-p) is run for n times; (such as if a coin is tossed for n times); there will be a little probability of getting all head, and there would be a little probability of getting all tails. A certain value of head and a certain value of tail would be maximal. This distribution is being called a binomial distribution.
Binomial distribution with checkerboard. image modified from WP
Poisson's distribution - example from Wikipedia: an individual keeping track of the amount of mail they receive each day may notice that they receive an average number of 4 letters per day. If mails are from independent source, then the number of pieces of mail received in a day obeys a Poisson distribution. i.e. there will be negligible chance for getting zero or 100 mail per day but a maximum of certain number (here 4) mail per day.
Similarly; suppose in an imaginary meadow e get around 10 pebbles in 1 km^2. With proportionally more area we get proportionally more pebbles. But for a certain 1 km^2 sample it is very unlikely to get 0 or 100 pebbles. probably it follows a Poisson's distribution.
According to Wikipedia, the number of decay events per second from a radioactive source, follows a Poisson's distribution.
Poisson's distribution from Wikipedia
Normal distribution or Gaussian distribution - if n number of dies rolled simultaneously, and given that n is very big; the sum of outcome of each dies would tend to be clustered around a central value. Not too big, not too small. This distribution is being called a normal distribution or bell shaped curve.
Sum of 2 dies, from here
With increasing number of simultaneous dies, the distribution approaches Gaussian. From central limit theorem
Similarly, if n number of coins tossed simultaneously, and n is very large, there would be a little chance we will get to many heads or too many tails. The number of heads will centre around a certain value. That is similar to binomial distribution but the number of coin is even larger.