In the era of digitization, Big Data has emerged as a phenomenon that is reshaping the business landscape. The sheer volume, velocity, and variety of data generated today are unprecedented, necessitating the role of Big Data consulting firms. These firms are adept at providing businesses with the necessary insights and strategies to harness this data's potential. With the ever-evolving data landscape, one might ask: What does the future hold for Big Data consulting firms?

Primarily, the role of Big Data consulting firms lies in helping businesses comprehend and utilize the vast amounts of data generated daily. With expertise in various data management technologies and statistical methodologies, these firms can extract valuable insights and trends from raw, unstructured data, thus enabling businesses to make strategic decisions.

In the realm of Big Data, one of the key concepts is 'Data Mining'. This process involves the extraction of patterns and knowledge from large volumes of data. It is a multidisciplinary subfield of computer science with an overall goal to extract information from a dataset and transform it into a comprehensible structure for further use. The relevance of data mining lies in its ability to help businesses identify patterns and predict future trends.

In terms of emerging trends, Machine Learning (ML) and Artificial Intelligence (AI) are revolutionizing Big Data consulting. Machine learning, a subset of AI, involves the use of statistical techniques to enable systems to 'learn' and improve from experience without being explicitly programmed. These technologies are amplifying the capabilities of Big Data consulting firms, allowing them to provide predictive analytics and advanced data modelling.

Another important trend is the advent of Edge Computing, which involves processing data near its source rather than transmitting it to a centralized cloud. This shift allows for faster processing times, lower latency, and improved data security. However, it also presents challenges in terms of infrastructure and data management, which Big Data consulting firms are well-equipped to tackle.

As for predictions about the future of Big Data consulting firms, one can expect them to play an increasingly vital role as businesses continue to generate and rely on large volumes of data. It is anticipated that these firms will evolve their capabilities, incorporating more sophisticated technologies like Quantum Computing, which promises exponential speed and processing power as compared to classical computing.

However, this is mere speculation. The future is never set in stone and is contingent on various factors such as technological advancements, regulatory changes, and market dynamics.

A cautionary note: the rise of these technologies also brings about certain ethical and legal dilemmas, such as data privacy and security, which Big Data consulting firms must address as they move forward.

In conclusion, Big Data consulting firms are at the forefront of the data revolution, providing businesses with the tools and strategies to harness the power of Big Data. With the rise of AI, ML, Edge Computing, and potentially Quantum Computing, the future looks promising for these firms. However, they must also tackle the ethical and legal challenges that these new technologies present, ensuring that data is used responsibly and securely. The combination of technical expertise and ethical stewardship will undoubtedly be the defining characteristic of successful Big Data consulting firms in the future.