Translation:The cat seems to want to play with the string.
"Vilja" is the infinitive form of "Vill".
Infinitive is a form of verbs that have many uses, one of them being that they are used after modal and auxiliary verbs.
English has infinitives as well, with similar usage as Swedish, but ours are harder to distinguish because they usually appear exactly the same as the present tense.
One way to distinguish between infinitives and present tense in English is to say the same sentence, but with a singular pronoun like "He/She", if the verb has an -S at the end, it's present tense.
For example, "Gå" is the infinitive of "Går":
"I go" -> "Jag går"
"She goes" -> "Han går"
"I can go" -> "Jag kan gå"
"He can go" -> "Han kan gå"