There are three forms of "research" you can perform on a Blueprint Original (BPO). You can copy a BPO to create a Blueprint Copy (BPC) with a certain number of Licensed Runs. BPOs are only able to be sold on the Market system. A BPC can be sold via the Contracts system or used to let friends and corpmates build items you have a BPO for without having to give away the actual BPO. You can improve a BPO in two ways. You can raise the Materiel Level of a blueprint to reduce it's waste amount and make it use less minerals to build. You can raise the Productivity Level of a blueprint to reduce the amount of time it takes to build from the blueprint. Materiel Level is often referred to as Materiel Efficency or ME and Productivity Level is often referred to as Productivity Efficency or PE (not to be confused with the Industry skill of the same initials Production Efficency, that skill actually reduces the minerals required based on the "ME" of a blueprint).
To improve or copy a BPO you will need the Science skill. Other skills will increase the speed at which you can improve or copy blueprints, for instance the Science skill gives a 5% bonus to copying speed of a blueprint per level. Metallurgy skill improves materiel efficency research speed 5% per level and the Research skill improves production time efficency research speed 5% per level. The Laboratory Operation skill will allow you to use an extra Research installation line per level of skill for improving multiple BPOs at once.
In Fig 1 & 2 you can see the Attributes and Bill of Materiels page for our example blueprint, Antimatter Charge S Blueprint. You can access this by right clicking on blueprint and using Show Info. The first figure shows three blueprints. The left most blueprint in Fig 1 is the original BPO as bought from the market. It hasn't been improved at all as you can see by the Materiel Level of 0, Wastage Factor of 0.1 and Productivity Level of 0 and a default Manufacturing Time of 2 minutes. Also note the "Copy No" and the Infinate Licensed Production Runs Remaining. You'll also note that my skills have reduced the Researching times in the middle down from their defaults.
The second blueprint in Fig 1 is an improved BPO. I've researched 50 Materiel Level runs and 20 Productivity Level runs. Note that the "PL" 20 has dropped the Manufacturing time down from 2 minutes per run to 1 minute, 37 seconds. Also note that the ML 50 has dropped the Wastage from 0.1 down to 0.002. In Fig 2 we'll see exactly how many minerals that saved us.
The third blueprint in Fig 1 is a 1000 Run copy BPC made from the improved BPO. Notice that it has the same values except it's marked as a Copy (Copy = YES) and has only 1000 Licensed Runs. A BPO viewed from the market will not show the line for Licensed Runs at all.
In Fig 2 we see the minerals required for both the orginial BPO and the improved BPO (remember the BPC is a copy of the improved BPO, so has the same stats). With a Material Level of 0 and a Wastage Factor of 0.1 we require 1 Nocxium, 17 Pyerite and 202 (212 with my Production Efficency skill level IV) Tritanium to build. You'd need more minerals with lower level PE skill. The improved BPO however only requires 1 Nocxium, 15 (16 w/PE IV) Pyerite and 184 (194 w/PE IV) Tritanium. So 50 runs of ML research saved us 2 Pyerite and 18 Tritanium! Doesn't sound like a lot, but when it's a ship BPO it can save you millions of ISK worth of minerals.