What is lag length? I've been looking up all across the internet to see what "lag length" is. 
I want to perform an Engle Granger - Augmented Dickey Fuller test, but for ADF, it always asks to specifiy a lag. It seems to me that whenever I look up lag length, most people just have trouble determining what it should be. 
What is the lag length? What does it mean?
 A: The lag length is how many terms back down the AR process you want to test for serial correlation. Is checking the prior one alone enough, or do you need to check in groups of 3, 4, or more. This page synopsizes the trade-offs for more or fewer lags.
A: Besides my comment above, according to this  the maximum lag length can be chosen by rule of a thumb formula:
$$
P_{max}=[12.(\frac{T}{100})^{1/4}]
$$
See page 121 in the above referenced link:

An important practical issue for the implementation of the ADF test is
  the speciﬁcation of the lag length p. If p is too small then the
  remaining serial correlation in the errors will bias the test. If p is
  too large then the power of the test will suﬀer. Ng and Perron (1995)
  suggest the following data dependent lag length selection procedure
  that results in stable size of the test and minimal power loss. First,
  set an upper bound pmax for p. Next, estimate the ADF test regression
  with p = pmax. If the absolute value of the t-statistic for testing
  the signiﬁcance of the last lagged diﬀerence is greater than 1.6 then
  set p = pmax and perform the unit root test. Otherwise, reduce the lag
  length by one and repeat the process. A useful rule of thumb for determining pmax, 
  suggested by Schwert(1989), is
$$
P_{max}=[12.(\frac{T}{100})^{1/4}]
$$

