In a standard monocurve world, the interest rate curve is increasing with decreasing slope. Something like this. This comes, in very basical environment, as the exponetial cumulative sum of spots rates.
Let me call the 10y-2y difference spread further on.
So why 10y-2y (in general)? This is a $long-short$ period difference. During a recessions, central banks lower rates pushing down the i.r. curve. When the spread starts contracting, market expects a coming cut of the i.r. and a future lower curve. For this reason, real world curves (vs academic ones) are decreasing on the long terms: a kind of economic cycle is implied. You may also read the spread under a credit risk point of view: a tight spread means "if an issuer can survive 2y, it is very likely that it will survive also 10y therefore a small extra premium is required". This is very clean in distressed bond issuers: implied yields usually form a reversed term structured (decreasing like an hyperbola).
Why 10y-2y (specific)? When bootstrapping i.r. curves you normally consider EONIA for very short terms, LIBORs and deposits for short terms ($<1y$), IRS for medium and long terms. This comes from the fact that is easy to find these instruments quoted on the market. In finance there are a lot of conventions, and this may be such one, but I think it comes from the fact that 10y is a very liquid proxy of long term (like in bond markets), meanwhile 2y is good and liquid proxy for short/medium term. Below 1y terms are too short to catch the credit/economic trends.