Pueden

Pueden is the third-person plural present indicative form of the Spanish verb poder, meaning "to be able to" or "can." It is used with subjects such as ellos, ellas, or ustedes and expresses ability, possibility, or permission in the present.

Poder is a stem-changing verb in the present tense. In most forms the stem changes from o to ue (poder → puedo, puedes, puede, podemos, podéis, pueden). The nosotros and vosotros forms use the less-change form pod- (podemos, podéis), while the other forms use pued- (puedo, puedes, puede, pueden). This pattern is a common feature of many verbs that express modality in Spanish.

Usage of pueden typically conveys present ability or possibility. It can appear with an infinitive to describe what someone or some group can do, as in "Ellos pueden bailar" (They can dance). It can also form questions or polite requests when combined with appropriate pronouns, such as "¿Pueden ustedes ayudarme?" (Can you all help me?). In regional varieties, ustedes often replaces vosotros as the plural you, and both can be followed by can/are able to.

Etymology traces poder to the Latin verb posse, meaning "to be able." The Spanish form pudieron/podían in the past reflects later evolution of the verb through Vulgar Latin.

In summary, pueden is a present-tense form indicating capability or possibility for a plural subject, derived from poder and sharing its functional role with other modality verbs in Spanish.