Translation:She looks like she needs to wash herself.
You can say it more like how it's said in English: Hon ser ut som att/om hon behöver tvätta sig 'She looks as if she needs to wash' – but then, just like in English, you don't get an infinitive but the present tense in the second half.
If you rewrite the sentence and switch verbs fromser ut and 'look like' to verka and 'appear', you can get the infinitive in the second part, too: Hon verkar behöva tvätta sig 'She seems to need to wash herself'.
Just a guess, and far from sure whether I'm wrong as I too am still learning, but I guess that “ser ut som” could only be followed by a noun, in order to describe an appearance; whereas the word “att” can only be followed by another verb, in order to write a subordinate clause describing the appearance.
Just my two cents. Maybe someone can explain it more correctly, and more comprehensibly.