便利 and 簡単: convenience and ease
Distinguish a useful, convenient tool from an easy procedure, including tools that are convenient but hard to learn.
Something convenient for a purpose
このアプリは予定の管理に便利です。 says that the app is convenient for managing a schedule. に with 便利, read べんり, marks the use for which it helps.
駅の近くに住むと、通勤に便利です。 says that living near a station is convenient for commuting. Convenience can come from location or access, not only low effort.
An easy or simple procedure
この料理は作り方が簡単です。 says that the recipe is simple to follow. 簡単, read かんたん, evaluates the lack of complexity or major difficulty.
簡単な説明をお願いします。 asks for a brief or simple explanation. It does not request an exhaustive, lengthy account of every detail.
Related but different judgments
便利な道具ですが、操作は簡単ではありません。 says that the tool is convenient but not easy to operate. Usefulness and difficulty of learning or operation are evaluated separately.
Before nouns, use な as in 便利な店 and 簡単な問題. 簡単に説明する means explaining briefly or simply and cannot automatically be replaced with 便利に.
Must a 便利な道具 also have 操作も簡単?
Show the answer and why
Not necessarily. A useful, convenient tool may still be difficult to operate. Convenience and difficulty are separate.