A word problem is a problem posed in plain language, as opposed to a problem with only "math" (equations, diagrams, graphs, etc.). Word problems are based on a contextualized scenario, often from real-life.
Translating Phrases to Math
Word problems often have phrases that indicate which math operation to use. For instance, the phrases "in total" and "altogether" are likely an indicator to use addition, while phrases like "take away" and "remaining" are likely an indicator to use subtraction.
Because word problems are based on a contextualized scenario, the context is important in interpreting the results. For instance, when determining the number of members per group when dividing 19 students into 4 teams, we shouldn't say that each team would get 4.75 students! However, we can say that when dividing 19 gallons of water into 4 jugs, each jug gets 4.75 gallons of water.
Especially if a problem is based on a real-life scenario, the context can help determine if an answer is reasonable. For instance, it would be unreasonable for someone to walk 60 miles per hour (without going into fictional characters like Sonic).