I have initially run a 2x2x2 Anova and found some significant interaction between the independent variables. I then ran a ANCOVA where I added a covariate. I am confused with how to interpret the output from the ANCOVA as the significant interactions that I found with the ANOVA are now insignificant in the ANCOVA.
First, the difference between significant and non-significant is not necessarily significant. So if after adding a covariate your interaction p-value changed from .04 to .06, this doesn't mean anything substantial other than you've bounced from one side of a binary .05 decision threshold.
However, the other possibility is that the covariate has substantially influenced the analysis. A typical motivation for including a covariate is that you want to control for its effect, and thereby adjust your estimates of main and interaction effects for the covariate.
I recommend that you produce a few plots of the cell mean both controlling and not controlling for the covariate to see what kind of difference inclusion of the covariates has made.