Something that is described as about to 'burst at the seams' is filled to capacity or has a very large amount to people or objects in it. 'Seams', are what keep clothing together so this expression conjures the image of clothing that is about to burst. 

1. Steven was so excited about going to the match he was almost bursting at the seams! I hope it lives up to his expectations.
2. So many people have moved into the city recently that it has begun to burst at the seams. The current infrastructure cannot cope with such numbers.
3. The train was bursting at the seams this morning. There was barely enough room to stand let alone sit.

1. We are going to need some more samples, the stand was bursting to the seams yesterday.
2. We want to get across that our food is bursting to the seams with freshness and nutrients.