As you train your Crew for their duties, you will find that they require a wide variety of equipment in order to improve their effectiveness. In most cases, you will need to build that equipment from components and lower-quality equipment that you have accumulated in your travels. Sometimes, however, you will need to venture back out in search of specific parts that you need.
In order to find a particular Item that you need for an equipment build, you will need to tap on that Item where it appears in the build plan. This will bring you to a menu where you can see a variety of Missions in which you could potentially obtain it. This could include Away Missions, Space Battles, and Transmissions for Shuttle Missions of a specific Faction.
A white-outlined chest indicated that the Item is a Standard Reward, and can be obtained by running that Mission or Battle. If it is an Away Mission or Space Battle, the Drop Chance shows you an abstract representation of how easy to acquire that Item might be, based on that missions's drop rate versus its cost (note: exact drop rates are never disclosed by us). For Transmissions, the odds of obtaining that Item will vary depending on your Reputation with the associated Faction.
A colored chest indicates that the Item is a Rare Reward, which is indicated along the Way Mission progression map by a star, and can only be claimed once. You will not be able to run this Mission multiple times to obtain more than one of this Item unless it also appears as a Standard Reward.
If none of these options are fully-accessible or ideal, you also have the option to Replicate the Item. The Replicator functions a number of times per day based on your VIP level, and allows you to expend Credits and other Items of various types in order to generate the Item you need. This option can theoretically be used to obtain any Item... except for that elusive Gold-Pressed Latinum, of course.