Translation:Oil makes you gain weight
There are two adjectives for "fat".
-nene is usually used for people
-nono is usually used for animals
The verb kunenepa means "to gain weight". I'm not exactly sure what this -pa suffix is as it seems to have disappeared and not be on many things, but it probably meant something like "become".
-esha is a causative suffix essentially meaning "make ...", so kunenep
esha means "to make (someone) gain weight", "to fatten"
Then we have the grammatical prefixes ... ya- is the subject prefix for class 6 (the 'plural' class of the ji-/ma- group, but a lot of ma- words are not really plural, such as mafuta), and the present tense -na-.
So to break it down we have:
"Oil is fattening."
commonly in verb conjugation (mnyambuliko wa vitenzi), the last syllable of the verb is changed to or added onto the suffix corresponding to the conjugated verb i.e. if you're doing the action, if the action is being done to you, if you and another person are doing it to each other e.t.c. It would be too long a lesson to summarize here, but it's covered pretty well on this website, along with other types of words: http://swa.gafkosoft.com/mnyambuliko_wa_vitenzi. it's a great resource
About the -pa suffix: it is archaic, but still lives on in a few words in Swahili (and other Bantu languages). It was used to change a noun or adjective to a verb (denomitative: https://en.wikipedia.org/wiki/Denominal_verb). Another Swahili example I found is kali (fierce) -> kukaripa ('be angry', not in TUKI) -> kukaripia, TUKI: 'to be angry at, to scold, to reprimand'
Another very strange example in this section! And like many of the other weight-related ones, the actual science is more complicated. For example, you can drink oil and not gain weight, and if you only drank oil, you would definitely lose weight (and probably die quite quickly).