Modal verbs usually accompany another verb in a sentence. They describe the subject in relation to the action expressed by the main verb.

"können" (can, be able) describes an ability or option.

Examples:
Harry kann Deutsch sprechen.
Sie können gerne ein anderes Zimmer haben.

You can also use "können" to make suggestions or polite requests by using the subjunctive II verb form.

Examples:
Anna: Wir könnten nach Leipzig fahren und Andersons Büro durchsuchen.
(= Not only does Anna consider it an option to go to Leipzig. In fact she thinks it's a good idea and suggests it to Harry.)

Student: Herr Professor, könnte ich Sie kurz sprechen?
(= The student would like to talk to the professor. He asks if that would be possible and requests a conversation. He could also say: "Kann ich Sie kurz sprechen?" But in the subjunctive II form it sounds more polite.)

The subjunctive II form of "können" is similar to the indicative past tense, in other words, by affixing (e)te + the personal endings. But in past tense the umlaut is omitted from the verb stem and in the subjunctive II it stays.