I was taught that certain consonants such as ш are always 'hard'. What function does the soft sign ь have when placed after these 'always hard' consonants? For example, in words such as учишься? Does ш + ь change the pronunciation of the ш? Or does it just indicate a pause?
The reason is purely historical.
Before the orthography reform of 1918, the two words mentioned by @КуЪ were written as тушъ and тушь, accordingly.
Those two writings are relics of the law of open syllables which, among other things, forbade the words to end with consonants in early Slavic languages.
The letters ъ and ь denoted reduced vowels present in Slavic languages at the time the Cyrillic alphabet was developed, and, though they later had either fallen or been transformed into full-length vowels both in Russian and in Russian rendition of Church Slavonic, the end-vowel rule had survived in Russian orthography (though it was not reflecting actual pronunciation anymore), because some kind of marking was required to distinguish words in pairs like мол/моль, кров/кровь and similar, where palatalization of the final consonant distinguishes between the meanings.
1918's reform retained ь in final positions for all words where it was historically present (including those ending with consonants not forming soft/hard pairs anymore), and dropped ъ in all final positions.
Other Slavic languages using Cyrillic had also undergone similar reforms: 1945's reform of Bulgarian orthography dropped both trailing ъ and ь (as all trailing Bulgarian consonants are hard), and 1847's reform of Serbian removed both ъ and ь from the alphabet at all (as only л, н, ц, ч and ж have hard/soft varieties in Serbian, the Serbs introduced separate letters for the each variety instead).
Some orthography reform projects (i. e. Fortunatov's 1912 project) suggested that final ь would be dropped after hard consonants as well, as the distinction it marks is only valid for but a few pairs and not represented at speech at all. However, none of those projects had passed so far.
All verbs and adverbs with trailing ж, ш and ч always have soft sign as the last character. It's just grammar rules, so soft sign in this cases has no function. In your example, "учишься" is derivative from "учишь".
You can read more info and make exercises here: http://www.gramota.ru/class/coach/tbgramota/45_88
- Глаголы с шипящим на конце всегда пишутся с мягким знаком. Например: СМОТРИШЬ или ПОСМОТРИШЬ (в форме второго лица ед. числа настоящего или будущего времени), РЕЖЬ (в повелительном наклонении), ЖЕЧЬ (в неопределенной форме). Обратите внимание, что в глаголах мягкий знак может оказаться после шипящей и не на самом конце слова, а перед постфиксами –СЯ или -ТЕ, например: КУПАЕШЬСЯ, СПРЯЧЬТЕ.