Citing data sources
Whenever you present your work -- whether on a website, in a published article, in a presesentation, or in a classroom assignment -- it is important to cite your sources. Citing a data source provides proper attribution and credit to the creators of a dataset, which is both a professional courtesy as well as an academic norm, and in some cases may actually be required by the data creator. Citing your sources also makes it easier for others to find those datasets and reuse them for their own research.
Cornell's Cornell Data Services provides a helpful guide to citing data. You'll want to be sure to cite any datasets that you use in your project, whether used for analysis or just display.
Citing a basemap
A basemap is a ready-made map layer that you can use underneath your own data layers to provide context for your data. Most basemaps are either cartographic products (like that on the left, showing placenames, boundaries, roads, etc.) or aerial images (like that on the right, which might include imagery from aircraft or satellites, and may or may not also include some placename labels):
If you use a basemap on your map, it is important to provide attribution for the basemap provider, and possibly the data sources that were used in the creation of that basemap.
In ArcMap, you can look at the layer properties for the basemap layer and copy the "Credits" text. For example, the credits for the World Street Map (on the left above) says: "Sources: Esri, HERE, Garmin, USGS, Intermap, INCREMENT P, NRCan, Esri Japan, METI, Esri China (Hong Kong), Esri Korea, Esri (Thailand), NGCC, (c) OpenStreetMap contributors, and the GIS User Community".
More details are available in this Esri FAQ: What is the correct way to cite an ArcGIS Online basemap?