- Month == JANis looking for two objects:- Month(found within- tuPeru1naomit) and- JAN(does not exist). I believe you intend to be looking for the value/string- "JAN", so- Month == "JAN".
 
- The third argument to - subset(..)is- select=, a non-standard-eval column selector. In your call, though, it appears that you are using it for a second subsetting condition. You need to combine your conditionals with- &(logical AND) or- |(logical OR), I'll assume the first.
 
subset(tuPeru1naomit, Month == "JAN" & YEAR == 1980)
#   Month YEAR  LONG   LAT    Temp
# 1   JAN 1980 -39.9 -89.5 17.5498
# 2   JAN 1980 -39.5 -89.5 17.8718
# 3   JAN 1980 -39.2 -89.5 18.1983
# 4   JAN 1980 -38.9 -89.5 18.5264
# 5   JAN 1980 -38.5 -89.5 18.8529
# 6   JAN 1980 -38.2 -89.5 19.1596
If you're curious about the use of the select= argument, all of the following are feasible options:
# range of columns
subset(tuPeru1naomit, Month == "JAN" & YEAR == 1980, select = LONG:Temp)
# individual columns, using non-standard-evaluation
subset(tuPeru1naomit, Month == "JAN" & YEAR == 1980, select = c(Month, LONG))
# same, using standard-evaluation (strings)
subset(tuPeru1naomit, Month == "JAN" & YEAR == 1980, select = c("Month", "LONG"))
# all except the specified columns
subset(tuPeru1naomit, Month == "JAN" & YEAR == 1980, select = -c(LONG))