Immunity can be a double edge sword. It is aimed to detect and destroy invading pathogens but it can also target the self, as exemplified in autoimmune diseases. To avoid this, many failsafe mechanisms exists.
For example, imagine an innocuous foreign antigen gets into your body and reaches the lymph node. There it may find a naive B cell that has a receptor that recognizes it. Without a double check mechanism this B cell will mature and begin to produce antibodies against this antigen, triggering an immune response that is not beneficial (e.g. in allergy) and is not necessary (the antigen is harmless).
Because of this, activation of the adaptive immune system requires usually two signals. In the context of B cells the other signal usually comes from effector CD4 T cells (of the type T follicular helper Tfh) and is called linked recognition, because both the naive B cell and the Tfh cell have to be specific for the same antigen.
So a possible scenario may look something like this: a pathogen's antigen is taken by DCs. If there is an ongoing inflammatory response this DCs will get fully activated (a process called licensing) and migrate to the lymph nodes. There they present the antigen to naive T cells. Naive T cells specific for the antigen mature and become effector T cells that may include CD8 and several classes of CD4 T cells, including CD4 Tfh cells. The antigen is also transported to the lymph nodes and presented to naive B cells. Naive B cells that recognize the antigen AND also are stimulated by Tfh specific for the same antigen then mature into plasma cells that secrete antibodies.
For harmless antigens, even though DCs may phagocyte them they will not get fully activated in the absence of an inflammatory response. So the activation chain is broken. This system fails somehow in the case of allergy.
Another point is that this mechanism is related to the generation of antibodies against microbial protein antigens. Animals lacking T cells cannot produce them and so they are called thymus-dependent (TD) antigens. Other microbial antigens like bacterial polysaccharides can induce antibody production without the help of T cells. This so called thymus-independent (TI) antigens provide the second signal by direct recognition of the antigen (e.g. through TLRs) or by inducing extensive crosslinking of B cell receptor (BCR). TI antigens include LPS and bacterial DNA. TI antigens appear earlier than TD antigens and although provide some protection they are less efficient than the TD ones because TI-specific B cells do not undergo affinity maturation and isotype class switching as TD antigens do.
Reference: Most of what I describe is found in Janeway's Immunobiology, 8th edition. Chapter 10 (The humoral immune response). In particular the section 10- "B-cell activation by helper T-cells".