To size up is to evaluate or critically assess something or someone. When a chess player sizes up her competition, she makes a judgment about what kind of player she might be facing.
If you're giving a speech, it might help to size up your audience before you decide to include your infamous corny jokes. And part of what happens during a job interview is that the interviewer sizes up the applicant, attempting to figure out what kind of worker they'd be. You could also size up the sofa your brother bought, guessing whether or not it's likely to fit through the front door.