I ran a Bayesian tree on Mr Bayes. Once convergence was reached I started to look at the trees. I first checked the standard output. Topology was more or less identical to the ML tree I obtained with PHYML but certain distances were really weird. Than I ran a consensus made of all compatible trees and this is really almost identical to my PHYML tree, however, posterior probabilities are not that nice. The default is 50% credibility or 50% majority. I do not fully understand what this means. So, one needs to make a consensus and I do understand this as 50% is like the 50% most probable trees. That correct? Can somebody explain what this means in non-statistical terms?
What you get depends on how you are constructing your consensus tree. There is a literature on how to summarize distributions of trees/bootstrap replicates (see this one among others), and the different methods produce different results. Some methods take a single tree and assign support values given that tree, whereas other methods produce a tree that has groups present in a certain percentage of the replicates/posterior and omits them otherwise.
A majority-rule consensus tree is the tree that contains a node present in at least half of the samples. This can be contrasted to a strict consensus tree (which requires nodes present in all samples) or a consensus tree using some other percentage (sometimes you see 70% or greater). A maximum clade credibility tree is related to this. You can calculate what's called "clade credibility" for a tree in the posterior distribution of trees, and the maximum clade credibility tree is the one with the largest. This is described in more detail in the link above.
As for your support values, it may be the case that there is discordance within your dataset that results in a tree with low support. You don't provide any details, so it's hard to assess. You could bootstrap your PhyML results and see whether poorly supported nodes from your MCC tree also have low bootstrap support within the scope of the ML analysis. However, if your (Bayesian) support values are around 0.5 (50%), these nodes are generally recognized as poorly supported and perhaps should be treated as unresolved.
Thanks for the clear and complete answer!