Round 1 , 2 ,3 etc are the different rounds for the colege counselling to get an admission.Admission in the colleges is done through your rank and marks in a specified examination. 
Lets take an example of JEE Mains. many students over India have given the examination. Now, they will have to join a college. For this, the will register in the counselling procedure providing all the Details. Different students will have different interest and choices. they will fill the form for counselling with their most favourite cllege and course  as the 1st choice and they will go on in a decreasing order.

Once you have your choices for the college and course , the colleges will check their seats and how many students have applied for each course.They will start with the students who has the lowest rank. these people will be offered a seat 1st. If you get a seat of your 1st choice, it is well and fine.You can go for the document verification and admission process of the college.

If not, you may or may not wait for an upgradation in the second round.

What happens in second round is that, may be some students who have been offered a seat by a particular college , donot join it. They wait for the second round to a get a better college. So, the seats are left vacant. then the colleges lower their cutoff for the next round ,so that the students who have ranks lower than those who applied in the 1st round can apply now for the left out seats.

this process goes on for the next rounds till all the seats get filled up or else the college decides to take a specified number of students this time.

So, it is better you aim to get a good rank to get an admission in a college of your choice.