Plant diversity has been shown to increase community biomass in experimental communities, but the mechanisms resulting in such positive biodiversity effects have remained largely unknown. We used a large‐scale six‐year biodiversity experiment near Jena, Germany, to examine how aboveground community biomass in grasslands is affected by different components of plant diversity and thereby infer the mechanisms that may underlie positive biodiversity effects. As components of diversity we defined the number of species (1–16), number of functional groups (1–4), presence of functional groups (legumes, tall herbs, small herbs, and grasses) and proportional abundance of functional groups. Using linear models, replacement series on the level of functional groups, and additive partitioning on the level of species, we explored whether the observed biodiversity effects originated from disproportionate effects of single functional groups or species or from positive interactions between them.Aboveground community biomass was positively related to the number of species measured across functional groups as well as to the number of functional groups measured across different levels of species richness. Furthermore, increasing the number of species within functional groups increased aboveground community biomass, indicating that species within functional groups were not redundant with respect to biomass production. A positive relationship between the number of functional groups and aboveground community biomass within a particular level of species richness suggested that complementarity was larger between species belonging to different rather than to the same functional groups. The presence of legumes or tall herbs had a strong positive impact on aboveground community biomass whereas the presence of small herbs or grasses had on average no significant effect. Two‐ and three‐way interactions between functional group presences were weak, suggesting that their main effects were largely additive. Replacement series analyses on the level of functional groups revealed strong transgressive overyielding and relative yields >1, indicating facilitation. On the species level, we found strong complementarity effects that increased over time while selection effects due to disproportionate contributions of particular species decreased over time. We conclude that transgressive overyielding between functional groups and species richness effects within functional groups caused the positive biodiversity effects on aboveground community biomass in our experiment.