Over 70% of the work you will do as a Data Scientist on any Data Science or Statistics project is cleaning your data and manipulating it to make it ready for modelling and analysis. 

What is Data Cleaning ?
At the start of a data science project, you will inherit multiple data-sets from different teams. You will then be asked to solve for a specific business problem. Your solution may not need all the data you got - you might have to remove columns, modify columns, remove duplicate values, deal with missing values, deal with outlier data etc. Sometimes you will also need to normalize or scale data to make the data fit within a range. 

This critical time consuming step is data cleaning or data cleansing. As part of the data cleansing process you will also perform EDA (Exploratory Data Analysis) - here you will visualise the data using graphs and statistical functions to understand the underlying data - mean, median, range, distribution etc. 

This Wikipedia explanation gives a good overview of Data Cleaning from a more generic perspective.

What is a pandas dataframe ?
Pandas is a software programming library in Python used for data analysis. Pandas provides data structures and tools for understanding and analysing data. 

The simplest way to understand a dataframe is to think of it as a MS Excel inside python. Just like how MS excel is used to store data, has rows/columns and you can perform operations on the data, similarly you can do all those with a dataframe. 

There are many ways to deal with data in python including series, lists and dictionaries, but dataframe is the structure of choice used by data scientists. Dataframes can deal with large amounts of data and support powerful functions to manipulate the data.