Reproduced from: hinduism.stackexchange.com/questions/5335/
tat karma yan na bandhāya => That (tat) is 'work' (karma), which (yat) is not (na) for the bondage (bandhāya). The expression "is for something" is often used in Sanskrit idiomatically to mean "leads to something", "causes something" or "transforms into something". Thus, a more idiomatic reading here would be "(Only) that is (real) 'work', which does not lead to bondage." Philosophically, this invokes the doctrine of performing one's duties, remaining detached from its results, and for that matter from everything else. The idea is that 'work' (karman), or performance of one's duties, is worth only if it is done observing proper detachment, and thus does not lead to attachment (i.e. "bondage") to this world.
sā vidyā yā vimuktaye => That (sā) is 'knowledge' (vidyā), which (yā) is for the liberation (vimuktaye). Again, this uses the same idiom as before, and thus really means: "(Only) that is (real) knowledge, which leads to liberation." Philosophically speaking, the liberation (vimukti/mokṣa) here refers to, at the very basic, to the emancipation from the cycle of (re-)birth and death. Thus the idea is that only that kind of knowledge and skill are worth, which lead to liberation from the worldly cycles of birth and death.
āyāsāyāparaṃ karma => For hardship/effort (āyāsāya) is the 'other work' (aparaṃ karma). As familiar to us by now, this really means: "All other kinds of work lead to hardship," i.e. works and duties performed with attachment (i.e. hoping for a certain result, or for the love of someone/something) lead, in the long run, to sufferings. There is a little bit more to add about the choice of the word "apara-". I translate it here as "other", which is indeed one of this common meanings, and also a relevant reading as will be apparent from the next part of the verse, but it also has another usage especially in philosophical contexts where it serves as the antonym to "para-" (absolute, higher, etc.) Thus, a typical usage is "parā vidyā" = the "higher knowledge", which refers to the transcendental/spiritual knowledge (that leads to vimukti), and in contrast, "aparā vidyā" = the other/lower knowledge, which refers to our worldly knowledge (which often leads to "bondage"). Thus, in this context both readings - "other/worldly duties/works" will be appropriate for "aparaṃ karma", without any real difference in the philosophical interpretation.
vidyānyā śilpanaipuṇam => The other (anyā) knowledge (vidyā) is skills in art/craft/etc. (śilpa-naipuṇam), i.e. the other kinds of knowledge are mere worldly skills, and hence are probably not even worth being called knowledge/vidyā.