A Festa Junina is much more than a harvest festival, but because of the timing of the festival and the popularity of these festivals in the Northeast of Brazil (where droughts are common), harvest foods play a large role, particularly those based around corn. The festivals are scheduled around the days of certain saints from the Catholic Church Joao, Pedro each which have certain meanings (harvest, rain, true love) and have become so popular that may parts of Brazil now celebrate Festas Julinas too.
Corn based offerings
Espiga de milho verde (corn on the cob)
canjicao (semi-sweet dish made with milk and hominy, with cinnamon)
pamonha (brazilian version of tamale, both sweet and savory versions exist)
mingao de milho verde (brazilian style creamed corn, also with cinnamon and of varying sweetness)
other brazilian dishes
acaraje (fritters made from bean meal, associated with baianas from Bahia traditionally fried in palm oil)
vatapa -- paste made with dried shrimp, peanuts, palm oil, coconut milk (served with acaraje)
pimenta malageta (not a dish per-se, but if you like your acaraje spicy)
churrasquinho (skewers, with beef, chicken, maybe sausage and hopefully cheese)
salgadinhos (savory treats, search on board for more descriptions)
pe-de-moleque (a brazilian peanut sweet, sort of a mix between fudge and brittle)
cocada (fudge made with coconut and condensed milk, served as cubes)
doce de leite (just like dulce de leche)
Quentao -- brazilian version of a hot toddy made with lime, cinnamon, cachaca, etc
(also beer, guarana, brazilian juices, and sodas)
cachorro quente (hot dog, but distinctly brazilian with many toppings such as corn sticks sort of like x-tudo and usually cooked in a tomato broth)
pipoca (brazilians do have pride in their own popcorn, but this will be made in the usual carnaval style poppers)
algodao doce (cotton candy)
There is usually a band and in the case of Somerville fireworks (probably more informal) which are traditional during such festivals. The quadrilha is a type of square dance done mostly to an arrastape beat (one rhythm of forro). There usually is a "country wedding" proceeding the quadrilha which might be hard to follow, but is humorous (often a noticably pregnant bride running away with her husband, being chased by her father with a shotgun, etc). You might get "arrested" by a 7 year old, led to a makeshift jail, and freed for a small donation to the church.
Most of these festivals start at 5pm and go until after 10pm, but Sunday ones are during the afternoon. If you are going for the chow, I would suggest going on the earlier side -- for Allston and Somerville 7-7:30 is probably good bet given that Brazilians run late. Keep the expectations in check as its a chance to experiment different foods, but quality can vary. Most of the churches sell tickets which you turn in for food (called a "ficha" in Portuguese). If you want a bit more excitement go later, but be patient with the crowds and be careful/respectful as its a different culture and now you are in the minority. Some of the festivals are larger and Somerville turns into an actual Brazilian block party.
Each year I try to come up with a list of the festivals, but this year I am having some trouble pinning down the dates. Here are the dates I have come up with so far. Cambridge is usually mid-month, Somerville at the end of the month, Everett after that, etc. Framingham was hosted by the Woodrow Wilson PTO (and last year was the same weekend as Allston), but I thought I saw something about it having been held during the school year.
Allston 6/7, Santo Antonio starting at 5pm: 43 Holton St - Allston, MA 02134
Lowell 6/21, Holy Family School, 5pm-1am 122 Andrews Street - Lowell - MA - 01852
Arrial de Cafe Belo: 6/15 A "festa junina" type festival outdoors at Cafe Belo in Somerville