What makes a password strong?
Length matters more than exotic characters: a 12 to 16 character password mixing letter cases and digits is harder to crack than a short one full of special characters. The generator shows the entropy and an estimated cracking time, so you can compare options against each other. Characters are taken from the operating system's cryptographically secure source of randomness, so no password can be predicted from the others the site has issued.
Does Randogram store the passwords it generates?
No. A password is produced on the server, returned in the response and never stored anywhere. The database keeps only the generation parameters — the password length, the selected character sets and the number of rows — but not the passwords themselves.
Can I reuse one password across several sites?
You should not: when one service leaks its database, attackers try the same login and password pair on every other site. Use a separate password for each service and keep them in a password manager rather than in a file or browser notes.