I keep hearing people use this term and have no idea what it means. I too popped into space in my HV once. How does this work? Is there a webpage someone can point me to?

Different playfields have different size limits- you can see these on the map or solar map in bottom right hand corner.

Upclassing refers to the fact that as you take damage more surfaces are openen meaning your size class increases as number of triangles rendered is the most important factor in size class. If for example the playfield is HV max size 1 and your HV is class size 1.49 (still class 1) as soon as it takes damage it will increase to 1.5 or higher (class 2) so you will be kicked from the playfield.

Therefore, when building or spawning ships ensure they are under the size class my a safe margin. You can test how size class increases in damage in creative or single player by shooting it or getting it shot. Some things tend to increase size class faster (for example I find checkerboard combat steel/carbon tends to increase size class faster as the carbon blocks are destroyed easily while the combat ones tend to stay but damaged. This increases size class faster.